In Ernst Kunz's ''commutative algebra and algebraic geometry'' book, ch.2, proposition 4.5 the author states:
Let $K$ be an algebraically closed field, $V\subset \mathbb{P}^n(K)$ a variety of dimension $d\geq 0$. Then in $\mathbb{P}^n(K)$ there are linear varieties $\Lambda_d$ and $\Lambda '_{n-d-1}$ respectively such that $\Lambda_d\cap\Lambda'_{n-d-1}=\emptyset, V\cap \Lambda'_{n-d-1} =\emptyset$, such that under the central projection from $\Lambda'_{n-d-1}, \space V$ is mapped $onto\space \Lambda_d$ and over any point of $\Lambda_d$ lie only finitely many points of $V$.
As hint, he says that the projection is defined as follows: For $P\in V$ the subspace spanned by $P$ and $\Lambda'_{n-d-1}$ is a linear variety of dimension $n-d$. It cuts $\Lambda_d$ in exactly one point $Q$, which by definition is the image of $P$.
But sadly I am unable to understand the hint as I am new to the projective business. Can someone kindly elaborate the hint, or give a (somewhat) detailed explanation, if possible?
Thanks in advance.